Compliance and Dynamic Modeling of General Notch Flexure Hinges Using a Beam Transfer Matrix

Ling, Mingxiang; Yuan, Lei; Lai, Jianhao; Wei, Huaxian; Zhang, Xianmin

doi:10.2139/ssrn.4199435

Cited by 4 publications

(5 citation statements)

References 22 publications

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“…1D straight-axis flexure hinges may be designed by using a segment whose longitudinal profile is defined by a single curve or by linking in series multiple segments of different longitudinal profiles. Several 1D hinge configurations have been studied in terms of their compliance or stiffness, including longitudinal profiles such as circular, elliptical, corner-filleted, conic-section, V-shaped, polynomial-curve, power-function, Bézier-curve or NURBS - [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The straightaxis flexure hinges quasi-static behavior has mainly been characterized by means of analytical and numerical methods, including the analytical compliance/stiffness matrix approach and the finite element technique - [4], the extended compliance matrix procedure - [5] and the discrete-beam transfer matrix method - [6].…”

Section: Introductionmentioning

confidence: 99%

“…Several 1D hinge configurations have been studied in terms of their compliance or stiffness, including longitudinal profiles such as circular, elliptical, corner-filleted, conic-section, V-shaped, polynomial-curve, power-function, Bézier-curve or NURBS - [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The straightaxis flexure hinges quasi-static behavior has mainly been characterized by means of analytical and numerical methods, including the analytical compliance/stiffness matrix approach and the finite element technique - [4], the extended compliance matrix procedure - [5] and the discrete-beam transfer matrix method - [6]. Expanding the deformation capabilities of straight-axis, 1D hinge configurations are the two-dimensional (2D) flexible hinges, which either are made of a single segment or combine segments with planar-curve longitudinal axes that may include straight-axis segments, as studied in [4] and [17][18][19][20][21][22][23][24], for instance.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

High-flexibility three-dimensional serial folded hinges

LOBONTIU,

MOSES,

HUNTER

2024

RJTS-AM

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A new three-dimensional flexible hinge capable of large, linear-domain displacements is proposed for extended spatial workspace mechanisms. The hinge structure is compact and modular consisting of a large number of circular- and straight-axis segments connected in series and disposed in two parallel planes in a folded manner. The analytical, linear-model compliance matrix, which is necessary in direct/inverse kinematics and controls analysis, is derived based on simplified hinge geometry and small-deformation theory. The compliance model is accurate, as demonstrated by finite element simulation and experimental testing of a prototype. The compliance model is also utilized to determine the hinge piston-motion stiffness and the static response of several hinges connected in series. Another analytical compliance model is formulated to predict the hinge maximum loads and displacements in terms of allowable stresses. The mathematical models are further utilized to comprehensively investigate the influence of geometric parameters on the hinge performance.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High-flexibility three-dimensional serial folded hinges

LOBONTIU,

MOSES,

HUNTER

2024

RJTS-AM

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“…The FBMM method proposed by Zhu et al 31 treats flexure hinges as series connections of finite micro beams, eliminating complex integration operations and improving modeling efficiency. However, on the shear effect of flexure hinges, the selection of shear coefficients is not uniform, and the obtained compliance model is not fully applicable to multiple-axis flexure hinges; Recently, also based on the idea of finite micro beams, Ling et al 32,33 proposed a generalized modeling method based on the finite-discrete and beam transfer matrix. However, this method requires knowledge of beam transfer matrix preparation and relatively complex matrix operations.…”

Section: Introductionmentioning

confidence: 99%

Development of novel multiple-axis flexure hinges based on hook function curve and a generalized model for multiple-axis flexure hinges

Du,

Liu,

2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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A novel asymmetric multiple-axis hook-function-curve (HFC) flexure hinge (HFCFH) with higher motion precision is proposed. For obtaining high-accuracy compliance and motion precision models of multiple-axis flexure hinges, a brief and generalized analytical model is presented by using the finite beam based matrix modeling (FBMM) method. It can be used to quickly obtain the compliance and precision models by just changing the notch contour functions. The comparative results prove the high accuracy and efficiency of the analytical model. For a much fairer comparison of motion precision between flexure hinges, a new precision model is proposed, in which a non-dimension and more intuitive precision matrix is defined. By using the precision model, the comparison of motion precision between multiple-axis HFCFHs and other multiple-axis flexure hinges indicates that asymmetric flexure hinges have higher motion precision, and multiple-axis HFCFHs also have higher motion precision in asymmetric flexure hinges. Based on the design concept of hybrid flexure hinges, eight types of hybrid multiple-axis flexure hinges with much higher performance are designed, enriching the types of multiple-axis flexure hinges and providing more reference for the selection of hinges in spatial compliant mechanisms.

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“…22,23 Note the fact that studies on transverse cross section showed a deficiency in the related literature compared to longitude cross section, namely cutting notch. Ling et al 24 derived the closed-form equations of compliance and axial drift targetting for single/multi-axis arbitrary-notched flexure hinges with a step-by-step modelling procedure. Li et al presented two generalized models for multi-axis flexure hinges with various notch contours.…”

Section: Introductionmentioning

confidence: 99%

Generalized model and performance analysis of elliptical-fillet cross-sectional flexure hinges

Yang

Yan

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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This work presents the design and analytical model of a novel flexure hinge with variable elliptical-fillet cross-section, which can be considered as an extension of existing results on rectangular and/or circular cross-sectional flexure hinges. The closed-form solutions in full degrees of freedom were derived for the compliance, rotational precision, and the maximum von Mises stress under various loads. To validate the analytical model, the theoretical results were compared with finite element analysis based on a set of parabolic notched flexure hinges. Finally, numerical simulations were conducted to evaluate the impact of the cross-sectional geometric parameters on the compliance and stress performance of the flexure hinges. The proposed method casts a unified framework on extended flexure hinges with a cross-sectional shape, which facilitates the systematic optimizations and performance evaluations of flexure hinges in various configurations.

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Compliance and Dynamic Modeling of General Notch Flexure Hinges Using a Beam Transfer Matrix

Cited by 4 publications

References 22 publications

High-flexibility three-dimensional serial folded hinges

High-flexibility three-dimensional serial folded hinges

Development of novel multiple-axis flexure hinges based on hook function curve and a generalized model for multiple-axis flexure hinges

Generalized model and performance analysis of elliptical-fillet cross-sectional flexure hinges

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